LMFDB - Embedded newform 9386.2.a.bw.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9386,2,Mod(1,9386)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9386.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9386 = 2 \cdot 13 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9386.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-15,-3,15,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$74.9475873372$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 27 x^{13} + 70 x^{12} + 306 x^{11} - 609 x^{10} - 1854 x^{9} + 2346 x^{8} + \cdots - 24 $ x^15 - 3x^14 - 27x^13 + 70x^12 + 306x^11 - 609x^10 - 1854x^9 + 2346x^8 + 6129x^7 - 3442x^6 - 9735x^5 + 222x^4 + 5181x^3 + 1422x^2 - 36x - 24
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.966809$ of defining polynomial
Character	$\chi$	$=$	9386.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +0.966809 q^{3} +1.00000 q^{4} +3.48601 q^{5} -0.966809 q^{6} +0.573182 q^{7} -1.00000 q^{8} -2.06528 q^{9} -3.48601 q^{10} -5.12586 q^{11} +0.966809 q^{12} +1.00000 q^{13} -0.573182 q^{14} +3.37030 q^{15} +1.00000 q^{16} +1.79074 q^{17} +2.06528 q^{18} +3.48601 q^{20} +0.554157 q^{21} +5.12586 q^{22} +7.66683 q^{23} -0.966809 q^{24} +7.15223 q^{25} -1.00000 q^{26} -4.89716 q^{27} +0.573182 q^{28} -3.24609 q^{29} -3.37030 q^{30} -6.22828 q^{31} -1.00000 q^{32} -4.95572 q^{33} -1.79074 q^{34} +1.99811 q^{35} -2.06528 q^{36} +1.06657 q^{37} +0.966809 q^{39} -3.48601 q^{40} -4.45685 q^{41} -0.554157 q^{42} -10.1992 q^{43} -5.12586 q^{44} -7.19958 q^{45} -7.66683 q^{46} -3.02020 q^{47} +0.966809 q^{48} -6.67146 q^{49} -7.15223 q^{50} +1.73130 q^{51} +1.00000 q^{52} -12.8340 q^{53} +4.89716 q^{54} -17.8688 q^{55} -0.573182 q^{56} +3.24609 q^{58} -12.1429 q^{59} +3.37030 q^{60} +1.43877 q^{61} +6.22828 q^{62} -1.18378 q^{63} +1.00000 q^{64} +3.48601 q^{65} +4.95572 q^{66} +12.7844 q^{67} +1.79074 q^{68} +7.41236 q^{69} -1.99811 q^{70} +8.87515 q^{71} +2.06528 q^{72} -16.7599 q^{73} -1.06657 q^{74} +6.91484 q^{75} -2.93805 q^{77} -0.966809 q^{78} -4.04246 q^{79} +3.48601 q^{80} +1.46123 q^{81} +4.45685 q^{82} +12.3393 q^{83} +0.554157 q^{84} +6.24253 q^{85} +10.1992 q^{86} -3.13835 q^{87} +5.12586 q^{88} -14.3513 q^{89} +7.19958 q^{90} +0.573182 q^{91} +7.66683 q^{92} -6.02155 q^{93} +3.02020 q^{94} -0.966809 q^{96} +9.77646 q^{97} +6.67146 q^{98} +10.5863 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{8} + 18 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} + 15 q^{16} + 3 q^{17} - 18 q^{18} + 3 q^{20} - 33 q^{21} + 3 q^{22} + 9 q^{23}+ \cdots + 3 q^{98}+O(q^{100}) $ 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 3 * q^5 + 3 * q^6 - 15 * q^8 + 18 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 + 15 * q^16 + 3 * q^17 - 18 * q^18 + 3 * q^20 - 33 * q^21 + 3 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 15 * q^26 - 42 * q^27 - 12 * q^29 - 24 * q^31 - 15 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 + 18 * q^36 - 30 * q^37 - 3 * q^39 - 3 * q^40 + 24 * q^41 + 33 * q^42 - 12 * q^43 - 3 * q^44 + 21 * q^45 - 9 * q^46 - 6 * q^47 - 3 * q^48 - 3 * q^49 - 24 * q^50 - 48 * q^51 + 15 * q^52 - 9 * q^53 + 42 * q^54 - 60 * q^55 + 12 * q^58 - 12 * q^59 - 12 * q^61 + 24 * q^62 + 15 * q^63 + 15 * q^64 + 3 * q^65 - 3 * q^66 - 48 * q^67 + 3 * q^68 - 18 * q^69 - 6 * q^70 - 21 * q^71 - 18 * q^72 + 21 * q^73 + 30 * q^74 - 21 * q^75 - 9 * q^77 + 3 * q^78 - 45 * q^79 + 3 * q^80 + 15 * q^81 - 24 * q^82 - 33 * q^83 - 33 * q^84 - 6 * q^85 + 12 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 - 21 * q^90 + 9 * q^92 - 3 * q^93 + 6 * q^94 + 3 * q^96 + 24 * q^97 + 3 * q^98

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.966809	0.558187	0.279094	−	0.960264i	$-0.409966\pi$
$3$	0.966809	0.558187	0.279094	+	0.960264i	$0.409966\pi$
$4$	1.00000	0.500000
$5$	3.48601	1.55899	0.779495	−	0.626409i	$-0.215476\pi$
$5$	3.48601	1.55899	0.779495	+	0.626409i	$0.215476\pi$
$6$	−0.966809	−0.394698
$7$	0.573182	0.216642	0.108321	−	0.994116i	$-0.465453\pi$
$7$	0.573182	0.216642	0.108321	+	0.994116i	$0.465453\pi$
$8$	−1.00000	−0.353553
$9$	−2.06528	−0.688427
$10$	−3.48601	−1.10237
$11$	−5.12586	−1.54550	−0.772752	−	0.634708i	$-0.781120\pi$
$11$	−5.12586	−1.54550	−0.772752	+	0.634708i	$0.781120\pi$
$12$	0.966809	0.279094
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.573182	−0.153189
$15$	3.37030	0.870208
$16$	1.00000	0.250000
$17$	1.79074	0.434319	0.217159	−	0.976136i	$-0.430321\pi$
$17$	1.79074	0.434319	0.217159	+	0.976136i	$0.430321\pi$
$18$	2.06528	0.486791
$19$	0	0
$19$	0	0
$20$	3.48601	0.779495
$21$	0.554157	0.120927
$22$	5.12586	1.09284
$23$	7.66683	1.59864	0.799322	−	0.600902i	$-0.205192\pi$
$23$	7.66683	1.59864	0.799322	+	0.600902i	$0.205192\pi$
$24$	−0.966809	−0.197349
$25$	7.15223	1.43045
$26$	−1.00000	−0.196116
$27$	−4.89716	−0.942458
$28$	0.573182	0.108321
$29$	−3.24609	−0.602785	−0.301392	−	0.953500i	$-0.597451\pi$
$29$	−3.24609	−0.602785	−0.301392	+	0.953500i	$0.597451\pi$
$30$	−3.37030	−0.615330
$31$	−6.22828	−1.11863	−0.559316	−	0.828955i	$-0.688936\pi$
$31$	−6.22828	−1.11863	−0.559316	+	0.828955i	$0.688936\pi$
$32$	−1.00000	−0.176777
$33$	−4.95572	−0.862681
$34$	−1.79074	−0.307110
$35$	1.99811	0.337743
$36$	−2.06528	−0.344213
$37$	1.06657	0.175343	0.0876716	−	0.996149i	$-0.472057\pi$
$37$	1.06657	0.175343	0.0876716	+	0.996149i	$0.472057\pi$
$38$	0	0
$39$	0.966809	0.154813
$40$	−3.48601	−0.551186
$41$	−4.45685	−0.696042	−0.348021	−	0.937487i	$-0.613146\pi$
$41$	−4.45685	−0.696042	−0.348021	+	0.937487i	$0.613146\pi$
$42$	−0.554157	−0.0855083
$43$	−10.1992	−1.55536	−0.777680	−	0.628660i	$-0.783604\pi$
$43$	−10.1992	−1.55536	−0.777680	+	0.628660i	$0.783604\pi$
$44$	−5.12586	−0.772752
$45$	−7.19958	−1.07325
$46$	−7.66683	−1.13041
$47$	−3.02020	−0.440541	−0.220270	−	0.975439i	$-0.570694\pi$
$47$	−3.02020	−0.440541	−0.220270	+	0.975439i	$0.570694\pi$
$48$	0.966809	0.139547
$49$	−6.67146	−0.953066
$50$	−7.15223	−1.01148
$51$	1.73130	0.242431
$52$	1.00000	0.138675
$53$	−12.8340	−1.76288	−0.881442	−	0.472293i	$-0.843426\pi$
$53$	−12.8340	−1.76288	−0.881442	+	0.472293i	$0.843426\pi$
$54$	4.89716	0.666419
$55$	−17.8688	−2.40942
$56$	−0.573182	−0.0765946
$57$	0	0
$58$	3.24609	0.426233
$59$	−12.1429	−1.58087	−0.790435	−	0.612546i	$-0.790146\pi$
$59$	−12.1429	−1.58087	−0.790435	+	0.612546i	$0.790146\pi$
$60$	3.37030	0.435104
$61$	1.43877	0.184216	0.0921081	−	0.995749i	$-0.470639\pi$
$61$	1.43877	0.184216	0.0921081	+	0.995749i	$0.470639\pi$
$62$	6.22828	0.790992
$63$	−1.18378	−0.149142
$64$	1.00000	0.125000
$65$	3.48601	0.432386
$66$	4.95572	0.610007
$67$	12.7844	1.56186	0.780930	−	0.624618i	$-0.214745\pi$
$67$	12.7844	1.56186	0.780930	+	0.624618i	$0.214745\pi$
$68$	1.79074	0.217159
$69$	7.41236	0.892343
$70$	−1.99811	−0.238820
$71$	8.87515	1.05329	0.526643	−	0.850086i	$-0.323450\pi$
$71$	8.87515	1.05329	0.526643	+	0.850086i	$0.323450\pi$
$72$	2.06528	0.243396
$73$	−16.7599	−1.96160	−0.980801	−	0.195013i	$-0.937525\pi$
$73$	−16.7599	−1.96160	−0.980801	+	0.195013i	$0.937525\pi$
$74$	−1.06657	−0.123986
$75$	6.91484	0.798457
$76$	0	0
$77$	−2.93805	−0.334821
$78$	−0.966809	−0.109470
$79$	−4.04246	−0.454812	−0.227406	−	0.973800i	$-0.573024\pi$
$79$	−4.04246	−0.454812	−0.227406	+	0.973800i	$0.573024\pi$
$80$	3.48601	0.389747
$81$	1.46123	0.162359
$82$	4.45685	0.492176
$83$	12.3393	1.35441	0.677207	−	0.735793i	$-0.263190\pi$
$83$	12.3393	1.35441	0.677207	+	0.735793i	$0.263190\pi$
$84$	0.554157	0.0604635
$85$	6.24253	0.677098
$86$	10.1992	1.09981
$87$	−3.13835	−0.336467
$88$	5.12586	0.546418
$89$	−14.3513	−1.52124	−0.760618	−	0.649200i	$-0.775104\pi$
$89$	−14.3513	−1.52124	−0.760618	+	0.649200i	$0.775104\pi$
$90$	7.19958	0.758902
$91$	0.573182	0.0600857
$92$	7.66683	0.799322
$93$	−6.02155	−0.624406
$94$	3.02020	0.311509
$95$	0	0
$96$	−0.966809	−0.0986745
$97$	9.77646	0.992649	0.496325	−	0.868137i	$-0.334683\pi$
$97$	9.77646	0.992649	0.496325	+	0.868137i	$0.334683\pi$
$98$	6.67146	0.673920
$99$	10.5863	1.06397
$100$	7.15223	0.715223
$101$	9.43674	0.938990	0.469495	−	0.882935i	$-0.344436\pi$
$101$	9.43674	0.938990	0.469495	+	0.882935i	$0.344436\pi$
$102$	−1.73130	−0.171425
$103$	−6.11332	−0.602363	−0.301182	−	0.953567i	$-0.597381\pi$
$103$	−6.11332	−0.602363	−0.301182	+	0.953567i	$0.597381\pi$
$104$	−1.00000	−0.0980581
$105$	1.93179	0.188524
$106$	12.8340	1.24655
$107$	−3.81753	−0.369054	−0.184527	−	0.982827i	$-0.559075\pi$
$107$	−3.81753	−0.369054	−0.184527	+	0.982827i	$0.559075\pi$
$108$	−4.89716	−0.471229
$109$	1.99936	0.191504	0.0957519	−	0.995405i	$-0.469474\pi$
$109$	1.99936	0.191504	0.0957519	+	0.995405i	$0.469474\pi$
$110$	17.8688	1.70372
$111$	1.03117	0.0978743
$112$	0.573182	0.0541606
$113$	−14.9780	−1.40902	−0.704508	−	0.709696i	$-0.748832\pi$
$113$	−14.9780	−1.40902	−0.704508	+	0.709696i	$0.748832\pi$
$114$	0	0
$115$	26.7266	2.49227
$116$	−3.24609	−0.301392
$117$	−2.06528	−0.190935
$118$	12.1429	1.11784
$119$	1.02642	0.0940918
$120$	−3.37030	−0.307665
$121$	15.2744	1.38858
$122$	−1.43877	−0.130261
$123$	−4.30892	−0.388522
$124$	−6.22828	−0.559316
$125$	7.50270	0.671062
$126$	1.18378	0.105460
$127$	0.00228665	0.000202908 0	0.000101454	−	1.00000i	$-0.499968\pi$
$127$	0.00228665	0.000202908 0	0.000101454		1.00000i	$0.499968\pi$
$128$	−1.00000	−0.0883883
$129$	−9.86066	−0.868182
$130$	−3.48601	−0.305743
$131$	4.07704	0.356213	0.178106	−	0.984011i	$-0.443003\pi$
$131$	4.07704	0.356213	0.178106	+	0.984011i	$0.443003\pi$
$132$	−4.95572	−0.431340
$133$	0	0
$134$	−12.7844	−1.10440
$135$	−17.0715	−1.46928
$136$	−1.79074	−0.153555
$137$	−0.258828	−0.0221131	−0.0110566	−	0.999939i	$-0.503519\pi$
$137$	−0.258828	−0.0221131	−0.0110566	+	0.999939i	$0.503519\pi$
$138$	−7.41236	−0.630982
$139$	−13.4185	−1.13814	−0.569072	−	0.822288i	$-0.692697\pi$
$139$	−13.4185	−1.13814	−0.569072	+	0.822288i	$0.692697\pi$
$140$	1.99811	0.168871
$141$	−2.91995	−0.245904
$142$	−8.87515	−0.744786
$143$	−5.12586	−0.428646
$144$	−2.06528	−0.172107
$145$	−11.3159	−0.939734
$146$	16.7599	1.38706
$147$	−6.45003	−0.531989
$148$	1.06657	0.0876716
$149$	18.1817	1.48950	0.744752	−	0.667342i	$-0.232568\pi$
$149$	18.1817	1.48950	0.744752	+	0.667342i	$0.232568\pi$
$150$	−6.91484	−0.564595
$151$	−0.924708	−0.0752517	−0.0376258	−	0.999292i	$-0.511980\pi$
$151$	−0.924708	−0.0752517	−0.0376258	+	0.999292i	$0.511980\pi$
$152$	0	0
$153$	−3.69838	−0.298997
$154$	2.93805	0.236755
$155$	−21.7118	−1.74393
$156$	0.966809	0.0774067
$157$	18.9510	1.51246	0.756228	−	0.654308i	$-0.227040\pi$
$157$	18.9510	1.51246	0.756228	+	0.654308i	$0.227040\pi$
$158$	4.04246	0.321601
$159$	−12.4080	−0.984019
$160$	−3.48601	−0.275593
$161$	4.39449	0.346334
$162$	−1.46123	−0.114805
$163$	−8.41510	−0.659121	−0.329561	−	0.944134i	$-0.606901\pi$
$163$	−8.41510	−0.659121	−0.329561	+	0.944134i	$0.606901\pi$
$164$	−4.45685	−0.348021
$165$	−17.2757	−1.34491
$166$	−12.3393	−0.957715
$167$	−24.0781	−1.86322	−0.931608	−	0.363465i	$-0.881594\pi$
$167$	−24.0781	−1.86322	−0.931608	+	0.363465i	$0.881594\pi$
$168$	−0.554157	−0.0427541
$169$	1.00000	0.0769231
$170$	−6.24253	−0.478781
$171$	0	0
$172$	−10.1992	−0.777680
$173$	−5.46891	−0.415794	−0.207897	−	0.978151i	$-0.566662\pi$
$173$	−5.46891	−0.415794	−0.207897	+	0.978151i	$0.566662\pi$
$174$	3.13835	0.237918
$175$	4.09953	0.309895
$176$	−5.12586	−0.386376
$177$	−11.7399	−0.882422
$178$	14.3513	1.07568
$179$	17.2183	1.28695	0.643477	−	0.765466i	$-0.277491\pi$
$179$	17.2183	1.28695	0.643477	+	0.765466i	$0.277491\pi$
$180$	−7.19958	−0.536625
$181$	−2.50468	−0.186172	−0.0930859	−	0.995658i	$-0.529673\pi$
$181$	−2.50468	−0.186172	−0.0930859	+	0.995658i	$0.529673\pi$
$182$	−0.573182	−0.0424870
$183$	1.39102	0.102827
$184$	−7.66683	−0.565206
$185$	3.71807	0.273358
$186$	6.02155	0.441522
$187$	−9.17908	−0.671241
$188$	−3.02020	−0.220270
$189$	−2.80696	−0.204176
$190$	0	0
$191$	−6.44008	−0.465988	−0.232994	−	0.972478i	$-0.574852\pi$
$191$	−6.44008	−0.465988	−0.232994	+	0.972478i	$0.574852\pi$
$192$	0.966809	0.0697734
$193$	−0.350714	−0.0252450	−0.0126225	−	0.999920i	$-0.504018\pi$
$193$	−0.350714	−0.0252450	−0.0126225	+	0.999920i	$0.504018\pi$
$194$	−9.77646	−0.701909
$195$	3.37030	0.241352
$196$	−6.67146	−0.476533
$197$	18.3450	1.30703	0.653514	−	0.756914i	$-0.273294\pi$
$197$	18.3450	1.30703	0.653514	+	0.756914i	$0.273294\pi$
$198$	−10.5863	−0.752338
$199$	−13.4103	−0.950628	−0.475314	−	0.879816i	$-0.657665\pi$
$199$	−13.4103	−0.950628	−0.475314	+	0.879816i	$0.657665\pi$
$200$	−7.15223	−0.505739
$201$	12.3601	0.871811
$202$	−9.43674	−0.663967
$203$	−1.86060	−0.130589
$204$	1.73130	0.121216
$205$	−15.5366	−1.08512
$206$	6.11332	0.425935
$207$	−15.8342	−1.10055
$208$	1.00000	0.0693375
$209$	0	0
$210$	−1.93179	−0.133306
$211$	−12.0269	−0.827964	−0.413982	−	0.910285i	$-0.635862\pi$
$211$	−12.0269	−0.827964	−0.413982	+	0.910285i	$0.635862\pi$
$212$	−12.8340	−0.881442
$213$	8.58057	0.587931
$214$	3.81753	0.260961
$215$	−35.5544	−2.42479
$216$	4.89716	0.333209
$217$	−3.56993	−0.242343
$218$	−1.99936	−0.135414
$219$	−16.2036	−1.09494
$220$	−17.8688	−1.20471
$221$	1.79074	0.120458
$222$	−1.03117	−0.0692076
$223$	−7.55163	−0.505694	−0.252847	−	0.967506i	$-0.581367\pi$
$223$	−7.55163	−0.505694	−0.252847	+	0.967506i	$0.581367\pi$
$224$	−0.573182	−0.0382973
$225$	−14.7714	−0.984758
$226$	14.9780	0.996325
$227$	−7.93349	−0.526564	−0.263282	−	0.964719i	$-0.584805\pi$
$227$	−7.93349	−0.526564	−0.263282	+	0.964719i	$0.584805\pi$
$228$	0	0
$229$	27.6864	1.82957	0.914786	−	0.403940i	$-0.132359\pi$
$229$	27.6864	1.82957	0.914786	+	0.403940i	$0.132359\pi$
$230$	−26.7266	−1.76230
$231$	−2.84053	−0.186893
$232$	3.24609	0.213117
$233$	7.47943	0.489994	0.244997	−	0.969524i	$-0.421213\pi$
$233$	7.47943	0.489994	0.244997	+	0.969524i	$0.421213\pi$
$234$	2.06528	0.135012
$235$	−10.5284	−0.686798
$236$	−12.1429	−0.790435
$237$	−3.90829	−0.253870
$238$	−1.02642	−0.0665329
$239$	14.9897	0.969600	0.484800	−	0.874625i	$-0.338892\pi$
$239$	14.9897	0.969600	0.484800	+	0.874625i	$0.338892\pi$
$240$	3.37030	0.217552
$241$	3.63720	0.234293	0.117146	−	0.993115i	$-0.462625\pi$
$241$	3.63720	0.234293	0.117146	+	0.993115i	$0.462625\pi$
$242$	−15.2744	−0.981876
$243$	16.1042	1.03308
$244$	1.43877	0.0921081
$245$	−23.2568	−1.48582
$246$	4.30892	0.274727
$247$	0	0
$248$	6.22828	0.395496
$249$	11.9297	0.756016
$250$	−7.50270	−0.474512
$251$	6.53728	0.412630	0.206315	−	0.978486i	$-0.433853\pi$
$251$	6.53728	0.412630	0.206315	+	0.978486i	$0.433853\pi$
$252$	−1.18378	−0.0745712
$253$	−39.2991	−2.47071
$254$	−0.00228665	−0.000143477 0
$255$	6.03534	0.377947
$256$	1.00000	0.0625000
$257$	−8.07867	−0.503934	−0.251967	−	0.967736i	$-0.581077\pi$
$257$	−8.07867	−0.503934	−0.251967	+	0.967736i	$0.581077\pi$
$258$	9.86066	0.613898
$259$	0.611339	0.0379867
$260$	3.48601	0.216193
$261$	6.70410	0.414973
$262$	−4.07704	−0.251881
$263$	−5.11911	−0.315658	−0.157829	−	0.987466i	$-0.550449\pi$
$263$	−5.11911	−0.315658	−0.157829	+	0.987466i	$0.550449\pi$
$264$	4.95572	0.305004
$265$	−44.7393	−2.74832
$266$	0	0
$267$	−13.8750	−0.849134
$268$	12.7844	0.780930
$269$	−2.44282	−0.148941	−0.0744707	−	0.997223i	$-0.523727\pi$
$269$	−2.44282	−0.148941	−0.0744707	+	0.997223i	$0.523727\pi$
$270$	17.0715	1.03894
$271$	3.37593	0.205073	0.102537	−	0.994729i	$-0.467304\pi$
$271$	3.37593	0.205073	0.102537	+	0.994729i	$0.467304\pi$
$272$	1.79074	0.108580
$273$	0.554157	0.0335391
$274$	0.258828	0.0156363
$275$	−36.6613	−2.21076
$276$	7.41236	0.446172
$277$	−0.453341	−0.0272386	−0.0136193	−	0.999907i	$-0.504335\pi$
$277$	−0.453341	−0.0272386	−0.0136193	+	0.999907i	$0.504335\pi$
$278$	13.4185	0.804789
$279$	12.8631	0.770096
$280$	−1.99811	−0.119410
$281$	13.5681	0.809403	0.404701	−	0.914449i	$-0.367376\pi$
$281$	13.5681	0.809403	0.404701	+	0.914449i	$0.367376\pi$
$282$	2.91995	0.173881
$283$	−7.28169	−0.432851	−0.216426	−	0.976299i	$-0.569440\pi$
$283$	−7.28169	−0.432851	−0.216426	+	0.976299i	$0.569440\pi$
$284$	8.87515	0.526643
$285$	0	0
$286$	5.12586	0.303098
$287$	−2.55458	−0.150792
$288$	2.06528	0.121698
$289$	−13.7932	−0.811367
$290$	11.3159	0.664493
$291$	9.45197	0.554084
$292$	−16.7599	−0.980801
$293$	−4.68665	−0.273797	−0.136899	−	0.990585i	$-0.543713\pi$
$293$	−4.68665	−0.273797	−0.136899	+	0.990585i	$0.543713\pi$
$294$	6.45003	0.376173
$295$	−42.3302	−2.46456
$296$	−1.06657	−0.0619932
$297$	25.1021	1.45657
$298$	−18.1817	−1.05324
$299$	7.66683	0.443384
$300$	6.91484	0.399229
$301$	−5.84598	−0.336957
$302$	0.924708	0.0532110
$303$	9.12352	0.524133
$304$	0	0
$305$	5.01558	0.287191
$306$	3.69838	0.211423
$307$	−11.8048	−0.673737	−0.336868	−	0.941552i	$-0.609368\pi$
$307$	−11.8048	−0.673737	−0.336868	+	0.941552i	$0.609368\pi$
$308$	−2.93805	−0.167411
$309$	−5.91041	−0.336232
$310$	21.7118	1.23315
$311$	8.00247	0.453779	0.226889	−	0.973921i	$-0.427144\pi$
$311$	8.00247	0.453779	0.226889	+	0.973921i	$0.427144\pi$
$312$	−0.966809	−0.0547348
$313$	13.4921	0.762617	0.381309	−	0.924448i	$-0.375474\pi$
$313$	13.4921	0.762617	0.381309	+	0.924448i	$0.375474\pi$
$314$	−18.9510	−1.06947
$315$	−4.12667	−0.232511
$316$	−4.04246	−0.227406
$317$	23.0549	1.29489	0.647445	−	0.762112i	$-0.275838\pi$
$317$	23.0549	1.29489	0.647445	+	0.762112i	$0.275838\pi$
$318$	12.4080	0.695806
$319$	16.6390	0.931606
$320$	3.48601	0.194874
$321$	−3.69082	−0.206001
$322$	−4.39449	−0.244895
$323$	0	0
$324$	1.46123	0.0811793
$325$	7.15223	0.396735
$326$	8.41510	0.466069
$327$	1.93300	0.106895
$328$	4.45685	0.246088
$329$	−1.73112	−0.0954398
$330$	17.2757	0.950995
$331$	−11.5092	−0.632604	−0.316302	−	0.948659i	$-0.602441\pi$
$331$	−11.5092	−0.632604	−0.316302	+	0.948659i	$0.602441\pi$
$332$	12.3393	0.677207
$333$	−2.20277	−0.120711
$334$	24.0781	1.31749
$335$	44.5664	2.43492
$336$	0.554157	0.0302317
$337$	0.595490	0.0324384	0.0162192	−	0.999868i	$-0.494837\pi$
$337$	0.595490	0.0324384	0.0162192	+	0.999868i	$0.494837\pi$
$338$	−1.00000	−0.0543928
$339$	−14.4809	−0.786495
$340$	6.24253	0.338549
$341$	31.9253	1.72885
$342$	0	0
$343$	−7.83623	−0.423117
$344$	10.1992	0.549903
$345$	25.8395	1.39115
$346$	5.46891	0.294010
$347$	−33.2481	−1.78485	−0.892426	−	0.451194i	$-0.850998\pi$
$347$	−33.2481	−1.78485	−0.892426	+	0.451194i	$0.850998\pi$
$348$	−3.13835	−0.168233
$349$	−8.52949	−0.456573	−0.228287	−	0.973594i	$-0.573312\pi$
$349$	−8.52949	−0.456573	−0.228287	+	0.973594i	$0.573312\pi$
$350$	−4.09953	−0.219129
$351$	−4.89716	−0.261391
$352$	5.12586	0.273209
$353$	35.2040	1.87372	0.936860	−	0.349704i	$-0.113718\pi$
$353$	35.2040	1.87372	0.936860	+	0.349704i	$0.113718\pi$
$354$	11.7399	0.623966
$355$	30.9388	1.64206
$356$	−14.3513	−0.760618
$357$	0.992352	0.0525208
$358$	−17.2183	−0.910013
$359$	−15.3519	−0.810240	−0.405120	−	0.914264i	$-0.632770\pi$
$359$	−15.3519	−0.810240	−0.405120	+	0.914264i	$0.632770\pi$
$360$	7.19958	0.379451
$361$	0	0
$362$	2.50468	0.131643
$363$	14.7674	0.775089
$364$	0.573182	0.0300429
$365$	−58.4252	−3.05812
$366$	−1.39102	−0.0727098
$367$	5.58516	0.291543	0.145772	−	0.989318i	$-0.453434\pi$
$367$	5.58516	0.291543	0.145772	+	0.989318i	$0.453434\pi$
$368$	7.66683	0.399661
$369$	9.20464	0.479174
$370$	−3.71807	−0.193293
$371$	−7.35620	−0.381915
$372$	−6.02155	−0.312203
$373$	−27.7786	−1.43832	−0.719161	−	0.694844i	$-0.755474\pi$
$373$	−27.7786	−1.43832	−0.719161	+	0.694844i	$0.755474\pi$
$374$	9.17908	0.474639
$375$	7.25368	0.374578
$376$	3.02020	0.155755
$377$	−3.24609	−0.167182
$378$	2.80696	0.144374
$379$	13.2768	0.681982	0.340991	−	0.940067i	$-0.389237\pi$
$379$	13.2768	0.681982	0.340991	+	0.940067i	$0.389237\pi$
$380$	0	0
$381$	0.00221076	0.000113261 0
$382$	6.44008	0.329503
$383$	−16.2254	−0.829079	−0.414539	−	0.910031i	$-0.636057\pi$
$383$	−16.2254	−0.829079	−0.414539	+	0.910031i	$0.636057\pi$
$384$	−0.966809	−0.0493373
$385$	−10.2420	−0.521983
$386$	0.350714	0.0178509
$387$	21.0642	1.07075
$388$	9.77646	0.496325
$389$	3.69557	0.187373	0.0936864	−	0.995602i	$-0.470135\pi$
$389$	3.69557	0.187373	0.0936864	+	0.995602i	$0.470135\pi$
$390$	−3.37030	−0.170662
$391$	13.7293	0.694321
$392$	6.67146	0.336960
$393$	3.94172	0.198833
$394$	−18.3450	−0.924208
$395$	−14.0920	−0.709047
$396$	10.5863	0.531983
$397$	−38.2776	−1.92110	−0.960549	−	0.278111i	$-0.910292\pi$
$397$	−38.2776	−1.92110	−0.960549	+	0.278111i	$0.910292\pi$
$398$	13.4103	0.672195
$399$	0	0
$400$	7.15223	0.357612
$401$	7.96776	0.397891	0.198946	−	0.980011i	$-0.436248\pi$
$401$	7.96776	0.397891	0.198946	+	0.980011i	$0.436248\pi$
$402$	−12.3601	−0.616463
$403$	−6.22828	−0.310253
$404$	9.43674	0.469495
$405$	5.09384	0.253115
$406$	1.86060	0.0923401
$407$	−5.46709	−0.270994
$408$	−1.73130	−0.0857123
$409$	−31.8345	−1.57411	−0.787057	−	0.616881i	$-0.788396\pi$
$409$	−31.8345	−1.57411	−0.787057	+	0.616881i	$0.788396\pi$
$410$	15.5366	0.767298
$411$	−0.250237	−0.0123433
$412$	−6.11332	−0.301182
$413$	−6.96008	−0.342483
$414$	15.8342	0.778206
$415$	43.0148	2.11152
$416$	−1.00000	−0.0490290
$417$	−12.9731	−0.635298
$418$	0	0
$419$	−7.13988	−0.348806	−0.174403	−	0.984674i	$-0.555800\pi$
$419$	−7.13988	−0.348806	−0.174403	+	0.984674i	$0.555800\pi$
$420$	1.93179	0.0942619
$421$	−15.4824	−0.754564	−0.377282	−	0.926098i	$-0.623141\pi$
$421$	−15.4824	−0.754564	−0.377282	+	0.926098i	$0.623141\pi$
$422$	12.0269	0.585459
$423$	6.23755	0.303280
$424$	12.8340	0.623273
$425$	12.8078	0.621270
$426$	−8.58057	−0.415730
$427$	0.824679	0.0399090
$428$	−3.81753	−0.184527
$429$	−4.95572	−0.239265
$430$	35.5544	1.71459
$431$	−35.0740	−1.68946	−0.844728	−	0.535196i	$-0.820238\pi$
$431$	−35.0740	−1.68946	−0.844728	+	0.535196i	$0.820238\pi$
$432$	−4.89716	−0.235615
$433$	5.19189	0.249506	0.124753	−	0.992188i	$-0.460186\pi$
$433$	5.19189	0.249506	0.124753	+	0.992188i	$0.460186\pi$
$434$	3.56993	0.171362
$435$	−10.9403	−0.524548
$436$	1.99936	0.0957519
$437$	0	0
$438$	16.2036	0.774240
$439$	31.1879	1.48852	0.744258	−	0.667892i	$-0.232803\pi$
$439$	31.1879	1.48852	0.744258	+	0.667892i	$0.232803\pi$
$440$	17.8688	0.851860
$441$	13.7784	0.656116
$442$	−1.79074	−0.0851769
$443$	−3.69892	−0.175741	−0.0878706	−	0.996132i	$-0.528006\pi$
$443$	−3.69892	−0.175741	−0.0878706	+	0.996132i	$0.528006\pi$
$444$	1.03117	0.0489372
$445$	−50.0287	−2.37159
$446$	7.55163	0.357580
$447$	17.5782	0.831422
$448$	0.573182	0.0270803
$449$	35.9049	1.69446	0.847228	−	0.531230i	$-0.178270\pi$
$449$	35.9049	1.69446	0.847228	+	0.531230i	$0.178270\pi$
$450$	14.7714	0.696329
$451$	22.8452	1.07574
$452$	−14.9780	−0.704508
$453$	−0.894016	−0.0420045
$454$	7.93349	0.372337
$455$	1.99811	0.0936730
$456$	0	0
$457$	4.74688	0.222050	0.111025	−	0.993818i	$-0.464587\pi$
$457$	4.74688	0.222050	0.111025	+	0.993818i	$0.464587\pi$
$458$	−27.6864	−1.29370
$459$	−8.76954	−0.409327
$460$	26.7266	1.24613
$461$	0.00970915	0.000452200 0	0.000226100	−	1.00000i	$-0.499928\pi$
$461$	0.00970915	0.000452200 0	0.000226100		1.00000i	$0.499928\pi$
$462$	2.84053	0.132153
$463$	−14.1936	−0.659634	−0.329817	−	0.944045i	$-0.606987\pi$
$463$	−14.1936	−0.659634	−0.329817	+	0.944045i	$0.606987\pi$
$464$	−3.24609	−0.150696
$465$	−20.9912	−0.973442
$466$	−7.47943	−0.346478
$467$	−19.6259	−0.908179	−0.454090	−	0.890956i	$-0.650035\pi$
$467$	−19.6259	−0.908179	−0.454090	+	0.890956i	$0.650035\pi$
$468$	−2.06528	−0.0954676
$469$	7.32777	0.338365
$470$	10.5284	0.485640
$471$	18.3220	0.844234
$472$	12.1429	0.558922
$473$	52.2795	2.40382
$474$	3.90829	0.179514
$475$	0	0
$476$	1.02642	0.0470459
$477$	26.5058	1.21362
$478$	−14.9897	−0.685611
$479$	20.8569	0.952974	0.476487	−	0.879181i	$-0.341910\pi$
$479$	20.8569	0.952974	0.476487	+	0.879181i	$0.341910\pi$
$480$	−3.37030	−0.153832
$481$	1.06657	0.0486314
$482$	−3.63720	−0.165670
$483$	4.24863	0.193319
$484$	15.2744	0.694291
$485$	34.0808	1.54753
$486$	−16.1042	−0.730501
$487$	−26.1602	−1.18543	−0.592715	−	0.805412i	$-0.701944\pi$
$487$	−26.1602	−1.18543	−0.592715	+	0.805412i	$0.701944\pi$
$488$	−1.43877	−0.0651303
$489$	−8.13579	−0.367913
$490$	23.2568	1.05063
$491$	−37.0128	−1.67036	−0.835182	−	0.549974i	$-0.814638\pi$
$491$	−37.0128	−1.67036	−0.835182	+	0.549974i	$0.814638\pi$
$492$	−4.30892	−0.194261
$493$	−5.81292	−0.261801
$494$	0	0
$495$	36.9040	1.65871
$496$	−6.22828	−0.279658
$497$	5.08707	0.228186
$498$	−11.9297	−0.534584
$499$	29.0035	1.29837	0.649186	−	0.760629i	$-0.275110\pi$
$499$	29.0035	1.29837	0.649186	+	0.760629i	$0.275110\pi$
$500$	7.50270	0.335531
$501$	−23.2789	−1.04002
$502$	−6.53728	−0.291773
$503$	−17.7812	−0.792822	−0.396411	−	0.918073i	$-0.629745\pi$
$503$	−17.7812	−0.792822	−0.396411	+	0.918073i	$0.629745\pi$
$504$	1.18378	0.0527298
$505$	32.8965	1.46388
$506$	39.2991	1.74706
$507$	0.966809	0.0429375
$508$	0.00228665	0.000101454 0
$509$	12.4185	0.550441	0.275220	−	0.961381i	$-0.411249\pi$
$509$	12.4185	0.550441	0.275220	+	0.961381i	$0.411249\pi$
$510$	−6.03534	−0.267249
$511$	−9.60648	−0.424966
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	8.07867	0.356335
$515$	−21.3111	−0.939078
$516$	−9.86066	−0.434091
$517$	15.4811	0.680858
$518$	−0.611339	−0.0268607
$519$	−5.28739	−0.232091
$520$	−3.48601	−0.152871
$521$	−27.8556	−1.22037	−0.610187	−	0.792257i	$-0.708906\pi$
$521$	−27.8556	−1.22037	−0.610187	+	0.792257i	$0.708906\pi$
$522$	−6.70410	−0.293430
$523$	18.0840	0.790760	0.395380	−	0.918518i	$-0.370613\pi$
$523$	18.0840	0.790760	0.395380	+	0.918518i	$0.370613\pi$
$524$	4.07704	0.178106
$525$	3.96346	0.172980
$526$	5.11911	0.223204
$527$	−11.1532	−0.485843
$528$	−4.95572	−0.215670
$529$	35.7803	1.55566
$530$	44.7393	1.94335
$531$	25.0785	1.08831
$532$	0	0
$533$	−4.45685	−0.193047
$534$	13.8750	0.600429
$535$	−13.3079	−0.575352
$536$	−12.7844	−0.552201
$537$	16.6468	0.718361
$538$	2.44282	0.105318
$539$	34.1970	1.47297
$540$	−17.0715	−0.734641
$541$	−10.7082	−0.460380	−0.230190	−	0.973146i	$-0.573935\pi$
$541$	−10.7082	−0.460380	−0.230190	+	0.973146i	$0.573935\pi$
$542$	−3.37593	−0.145009
$543$	−2.42155	−0.103919
$544$	−1.79074	−0.0767774
$545$	6.96977	0.298552
$546$	−0.554157	−0.0237157
$547$	3.52018	0.150512	0.0752561	−	0.997164i	$-0.476023\pi$
$547$	3.52018	0.150512	0.0752561	+	0.997164i	$0.476023\pi$
$548$	−0.258828	−0.0110566
$549$	−2.97147	−0.126819
$550$	36.6613	1.56324
$551$	0	0
$552$	−7.41236	−0.315491
$553$	−2.31706	−0.0985316
$554$	0.453341	0.0192606
$555$	3.59466	0.152585
$556$	−13.4185	−0.569072
$557$	28.3353	1.20060	0.600302	−	0.799773i	$-0.295047\pi$
$557$	28.3353	1.20060	0.600302	+	0.799773i	$0.295047\pi$
$558$	−12.8631	−0.544540
$559$	−10.1992	−0.431379
$560$	1.99811	0.0844357
$561$	−8.87442	−0.374678
$562$	−13.5681	−0.572334
$563$	31.8537	1.34247	0.671236	−	0.741243i	$-0.265764\pi$
$563$	31.8537	1.34247	0.671236	+	0.741243i	$0.265764\pi$
$564$	−2.91995	−0.122952
$565$	−52.2135	−2.19664
$566$	7.28169	0.306072
$567$	0.837548	0.0351737
$568$	−8.87515	−0.372393
$569$	−12.0558	−0.505405	−0.252703	−	0.967544i	$-0.581319\pi$
$569$	−12.0558	−0.505405	−0.252703	+	0.967544i	$0.581319\pi$
$570$	0	0
$571$	−19.8282	−0.829783	−0.414892	−	0.909871i	$-0.636180\pi$
$571$	−19.8282	−0.829783	−0.414892	+	0.909871i	$0.636180\pi$
$572$	−5.12586	−0.214323
$573$	−6.22633	−0.260109
$574$	2.55458	0.106626
$575$	54.8350	2.28678
$576$	−2.06528	−0.0860534
$577$	40.4738	1.68495	0.842474	−	0.538737i	$-0.181098\pi$
$577$	40.4738	1.68495	0.842474	+	0.538737i	$0.181098\pi$
$578$	13.7932	0.573723
$579$	−0.339074	−0.0140914
$580$	−11.3159	−0.469867
$581$	7.07265	0.293423
$582$	−9.45197	−0.391797
$583$	65.7852	2.72454
$584$	16.7599	0.693531
$585$	−7.19958	−0.297666
$586$	4.68665	0.193604
$587$	−19.5138	−0.805421	−0.402710	−	0.915327i	$-0.631932\pi$
$587$	−19.5138	−0.805421	−0.402710	+	0.915327i	$0.631932\pi$
$588$	−6.45003	−0.265995
$589$	0	0
$590$	42.3302	1.74271
$591$	17.7361	0.729566
$592$	1.06657	0.0438358
$593$	−4.50096	−0.184832	−0.0924161	−	0.995720i	$-0.529459\pi$
$593$	−4.50096	−0.184832	−0.0924161	+	0.995720i	$0.529459\pi$
$594$	−25.1021	−1.02995
$595$	3.57811	0.146688
$596$	18.1817	0.744752
$597$	−12.9652	−0.530628
$598$	−7.66683	−0.313520
$599$	5.74887	0.234892	0.117446	−	0.993079i	$-0.462529\pi$
$599$	5.74887	0.234892	0.117446	+	0.993079i	$0.462529\pi$
$600$	−6.91484	−0.282297
$601$	21.1196	0.861487	0.430744	−	0.902474i	$-0.358251\pi$
$601$	21.1196	0.861487	0.430744	+	0.902474i	$0.358251\pi$
$602$	5.84598	0.238264
$603$	−26.4033	−1.07523
$604$	−0.924708	−0.0376258
$605$	53.2467	2.16479
$606$	−9.12352	−0.370618
$607$	−20.5668	−0.834782	−0.417391	−	0.908727i	$-0.637055\pi$
$607$	−20.5668	−0.834782	−0.417391	+	0.908727i	$0.637055\pi$
$608$	0	0
$609$	−1.79885	−0.0728929
$610$	−5.01558	−0.203075
$611$	−3.02020	−0.122184
$612$	−3.69838	−0.149498
$613$	−31.6690	−1.27910	−0.639550	−	0.768749i	$-0.720879\pi$
$613$	−31.6690	−1.27910	−0.639550	+	0.768749i	$0.720879\pi$
$614$	11.8048	0.476404
$615$	−15.0209	−0.605702
$616$	2.93805	0.118377
$617$	−21.0511	−0.847486	−0.423743	−	0.905783i	$-0.639284\pi$
$617$	−21.0511	−0.847486	−0.423743	+	0.905783i	$0.639284\pi$
$618$	5.91041	0.237752
$619$	−2.66809	−0.107240	−0.0536199	−	0.998561i	$-0.517076\pi$
$619$	−2.66809	−0.107240	−0.0536199	+	0.998561i	$0.517076\pi$
$620$	−21.7118	−0.871967
$621$	−37.5457	−1.50666
$622$	−8.00247	−0.320870
$623$	−8.22590	−0.329564
$624$	0.966809	0.0387033
$625$	−9.60672	−0.384269
$626$	−13.4921	−0.539252
$627$	0	0
$628$	18.9510	0.756228
$629$	1.90995	0.0761548
$630$	4.12667	0.164410
$631$	−46.2028	−1.83930	−0.919652	−	0.392735i	$-0.871529\pi$
$631$	−46.2028	−1.83930	−0.919652	+	0.392735i	$0.871529\pi$
$632$	4.04246	0.160800
$633$	−11.6277	−0.462159
$634$	−23.0549	−0.915626
$635$	0.00797129	0.000316331 0
$636$	−12.4080	−0.492009
$637$	−6.67146	−0.264333
$638$	−16.6390	−0.658745
$639$	−18.3297	−0.725111
$640$	−3.48601	−0.137796
$641$	−1.58556	−0.0626257	−0.0313129	−	0.999510i	$-0.509969\pi$
$641$	−1.58556	−0.0626257	−0.0313129	+	0.999510i	$0.509969\pi$
$642$	3.69082	0.145665
$643$	−25.6417	−1.01121	−0.505605	−	0.862765i	$-0.668731\pi$
$643$	−25.6417	−1.01121	−0.505605	+	0.862765i	$0.668731\pi$
$644$	4.39449	0.173167
$645$	−34.3743	−1.35349
$646$	0	0
$647$	−18.3543	−0.721583	−0.360792	−	0.932646i	$-0.617493\pi$
$647$	−18.3543	−0.721583	−0.360792	+	0.932646i	$0.617493\pi$
$648$	−1.46123	−0.0574024
$649$	62.2427	2.44324
$650$	−7.15223	−0.280534
$651$	−3.45144	−0.135273
$652$	−8.41510	−0.329561
$653$	27.3920	1.07193	0.535966	−	0.844239i	$-0.319947\pi$
$653$	27.3920	1.07193	0.535966	+	0.844239i	$0.319947\pi$
$654$	−1.93300	−0.0755862
$655$	14.2126	0.555332
$656$	−4.45685	−0.174011
$657$	34.6140	1.35042
$658$	1.73112	0.0674861
$659$	26.2346	1.02196	0.510978	−	0.859594i	$-0.329283\pi$
$659$	26.2346	1.02196	0.510978	+	0.859594i	$0.329283\pi$
$660$	−17.2757	−0.672455
$661$	14.7472	0.573598	0.286799	−	0.957991i	$-0.407409\pi$
$661$	14.7472	0.573598	0.286799	+	0.957991i	$0.407409\pi$
$662$	11.5092	0.447318
$663$	1.73130	0.0672383
$664$	−12.3393	−0.478857
$665$	0	0
$666$	2.20277	0.0853555
$667$	−24.8873	−0.963638
$668$	−24.0781	−0.931608
$669$	−7.30098	−0.282272
$670$	−44.5664	−1.72175
$671$	−7.37495	−0.284707
$672$	−0.554157	−0.0213771
$673$	25.1045	0.967709	0.483854	−	0.875149i	$-0.339236\pi$
$673$	25.1045	0.967709	0.483854	+	0.875149i	$0.339236\pi$
$674$	−0.595490	−0.0229374
$675$	−35.0256	−1.34814
$676$	1.00000	0.0384615
$677$	6.25280	0.240315	0.120157	−	0.992755i	$-0.461660\pi$
$677$	6.25280	0.240315	0.120157	+	0.992755i	$0.461660\pi$
$678$	14.4809	0.556136
$679$	5.60369	0.215050
$680$	−6.24253	−0.239390
$681$	−7.67017	−0.293921
$682$	−31.9253	−1.22248
$683$	−36.9876	−1.41529	−0.707645	−	0.706568i	$-0.750242\pi$
$683$	−36.9876	−1.41529	−0.707645	+	0.706568i	$0.750242\pi$
$684$	0	0
$685$	−0.902274	−0.0344741
$686$	7.83623	0.299189
$687$	26.7675	1.02124
$688$	−10.1992	−0.388840
$689$	−12.8340	−0.488936
$690$	−25.8395	−0.983694
$691$	24.2271	0.921643	0.460821	−	0.887493i	$-0.347555\pi$
$691$	24.2271	0.921643	0.460821	+	0.887493i	$0.347555\pi$
$692$	−5.46891	−0.207897
$693$	6.06789	0.230500
$694$	33.2481	1.26208
$695$	−46.7770	−1.77435
$696$	3.13835	0.118959
$697$	−7.98106	−0.302304
$698$	8.52949	0.322846
$699$	7.23118	0.273508
$700$	4.09953	0.154948
$701$	−24.1094	−0.910598	−0.455299	−	0.890339i	$-0.650468\pi$
$701$	−24.1094	−0.910598	−0.455299	+	0.890339i	$0.650468\pi$
$702$	4.89716	0.184831
$703$	0	0
$704$	−5.12586	−0.193188
$705$	−10.1790	−0.383362
$706$	−35.2040	−1.32492
$707$	5.40896	0.203425
$708$	−11.7399	−0.441211
$709$	−10.5363	−0.395700	−0.197850	−	0.980232i	$-0.563396\pi$
$709$	−10.5363	−0.395700	−0.197850	+	0.980232i	$0.563396\pi$
$710$	−30.9388	−1.16111
$711$	8.34881	0.313105
$712$	14.3513	0.537838
$713$	−47.7512	−1.78829
$714$	−0.992352	−0.0371378
$715$	−17.8688	−0.668254
$716$	17.2183	0.643477
$717$	14.4921	0.541219
$718$	15.3519	0.572926
$719$	−44.7780	−1.66994	−0.834969	−	0.550298i	$-0.814514\pi$
$719$	−44.7780	−1.66994	−0.834969	+	0.550298i	$0.814514\pi$
$720$	−7.19958	−0.268313
$721$	−3.50404	−0.130497
$722$	0	0
$723$	3.51648	0.130779
$724$	−2.50468	−0.0930859
$725$	−23.2168	−0.862251
$726$	−14.7674	−0.548071
$727$	−21.0982	−0.782488	−0.391244	−	0.920287i	$-0.627955\pi$
$727$	−21.0982	−0.782488	−0.391244	+	0.920287i	$0.627955\pi$
$728$	−0.573182	−0.0212435
$729$	11.1860	0.414296
$730$	58.4252	2.16241
$731$	−18.2641	−0.675522
$732$	1.39102	0.0514136
$733$	49.0116	1.81029	0.905143	−	0.425108i	$-0.139764\pi$
$733$	49.0116	1.81029	0.905143	+	0.425108i	$0.139764\pi$
$734$	−5.58516	−0.206152
$735$	−22.4848	−0.829366
$736$	−7.66683	−0.282603
$737$	−65.5309	−2.41386
$738$	−9.20464	−0.338827
$739$	−6.60219	−0.242865	−0.121433	−	0.992600i	$-0.538749\pi$
$739$	−6.60219	−0.242865	−0.121433	+	0.992600i	$0.538749\pi$
$740$	3.71807	0.136679
$741$	0	0
$742$	7.35620	0.270055
$743$	−36.8012	−1.35011	−0.675053	−	0.737769i	$-0.735879\pi$
$743$	−36.8012	−1.35011	−0.675053	+	0.737769i	$0.735879\pi$
$744$	6.02155	0.220761
$745$	63.3815	2.32212
$746$	27.7786	1.01705
$747$	−25.4841	−0.932415
$748$	−9.17908	−0.335621
$749$	−2.18814	−0.0799528
$750$	−7.25368	−0.264867
$751$	39.4647	1.44009	0.720044	−	0.693929i	$-0.244122\pi$
$751$	39.4647	1.44009	0.720044	+	0.693929i	$0.244122\pi$
$752$	−3.02020	−0.110135
$753$	6.32030	0.230325
$754$	3.24609	0.118216
$755$	−3.22354	−0.117317
$756$	−2.80696	−0.102088
$757$	−20.8335	−0.757207	−0.378603	−	0.925559i	$-0.623596\pi$
$757$	−20.8335	−0.757207	−0.378603	+	0.925559i	$0.623596\pi$
$758$	−13.2768	−0.482234
$759$	−37.9947	−1.37912
$760$	0	0
$761$	−3.40954	−0.123596	−0.0617978	−	0.998089i	$-0.519683\pi$
$761$	−3.40954	−0.123596	−0.0617978	+	0.998089i	$0.519683\pi$
$762$	−0.00221076	−8.00873e−5 0
$763$	1.14600	0.0414878
$764$	−6.44008	−0.232994
$765$	−12.8926	−0.466132
$766$	16.2254	0.586247
$767$	−12.1429	−0.438455
$768$	0.966809	0.0348867
$769$	35.3080	1.27324	0.636620	−	0.771178i	$-0.280332\pi$
$769$	35.3080	1.27324	0.636620	+	0.771178i	$0.280332\pi$
$770$	10.2420	0.369098
$771$	−7.81053	−0.281289
$772$	−0.350714	−0.0126225
$773$	−11.6068	−0.417466	−0.208733	−	0.977973i	$-0.566934\pi$
$773$	−11.6068	−0.417466	−0.208733	+	0.977973i	$0.566934\pi$
$774$	−21.0642	−0.757136
$775$	−44.5461	−1.60014
$776$	−9.77646	−0.350954
$777$	0.591048	0.0212037
$778$	−3.69557	−0.132493
$779$	0	0
$780$	3.37030	0.120676
$781$	−45.4927	−1.62786
$782$	−13.7293	−0.490959
$783$	15.8966	0.568099
$784$	−6.67146	−0.238267
$785$	66.0634	2.35790
$786$	−3.94172	−0.140597
$787$	−2.91361	−0.103859	−0.0519295	−	0.998651i	$-0.516537\pi$
$787$	−2.91361	−0.103859	−0.0519295	+	0.998651i	$0.516537\pi$
$788$	18.3450	0.653514
$789$	−4.94920	−0.176196
$790$	14.0920	0.501372
$791$	−8.58514	−0.305252
$792$	−10.5863	−0.376169
$793$	1.43877	0.0510924
$794$	38.2776	1.35842
$795$	−43.2544	−1.53407
$796$	−13.4103	−0.475314
$797$	−33.1674	−1.17485	−0.587426	−	0.809278i	$-0.699859\pi$
$797$	−33.1674	−1.17485	−0.587426	+	0.809278i	$0.699859\pi$
$798$	0	0
$799$	−5.40839	−0.191335
$800$	−7.15223	−0.252870
$801$	29.6395	1.04726
$802$	−7.96776	−0.281352
$803$	85.9090	3.03166
$804$	12.3601	0.435905
$805$	15.3192	0.539931
$806$	6.22828	0.219382
$807$	−2.36174	−0.0831373
$808$	−9.43674	−0.331983
$809$	21.5983	0.759357	0.379678	−	0.925119i	$-0.376035\pi$
$809$	21.5983	0.759357	0.379678	+	0.925119i	$0.376035\pi$
$810$	−5.09384	−0.178979
$811$	−31.3858	−1.10210	−0.551052	−	0.834471i	$-0.685773\pi$
$811$	−31.3858	−1.10210	−0.551052	+	0.834471i	$0.685773\pi$
$812$	−1.86060	−0.0652943
$813$	3.26388	0.114469
$814$	5.46709	0.191621
$815$	−29.3351	−1.02756
$816$	1.73130	0.0606078
$817$	0	0
$818$	31.8345	1.11307
$819$	−1.18378	−0.0413646
$820$	−15.5366	−0.542561
$821$	−48.1093	−1.67903	−0.839513	−	0.543339i	$-0.817160\pi$
$821$	−48.1093	−1.67903	−0.839513	+	0.543339i	$0.817160\pi$
$822$	0.250237	0.00872801
$823$	−10.4224	−0.363302	−0.181651	−	0.983363i	$-0.558144\pi$
$823$	−10.4224	−0.363302	−0.181651	+	0.983363i	$0.558144\pi$
$824$	6.11332	0.212968
$825$	−35.4445	−1.23402
$826$	6.96008	0.242172
$827$	41.1559	1.43113	0.715566	−	0.698545i	$-0.246169\pi$
$827$	41.1559	1.43113	0.715566	+	0.698545i	$0.246169\pi$
$828$	−15.8342	−0.550275
$829$	23.7120	0.823550	0.411775	−	0.911285i	$-0.364909\pi$
$829$	23.7120	0.823550	0.411775	+	0.911285i	$0.364909\pi$
$830$	−43.0148	−1.49307
$831$	−0.438294	−0.0152042
$832$	1.00000	0.0346688
$833$	−11.9469	−0.413934
$834$	12.9731	0.449223
$835$	−83.9362	−2.90473
$836$	0	0
$837$	30.5009	1.05426
$838$	7.13988	0.246643
$839$	−26.2168	−0.905105	−0.452553	−	0.891738i	$-0.649487\pi$
$839$	−26.2168	−0.905105	−0.452553	+	0.891738i	$0.649487\pi$
$840$	−1.93179	−0.0666532
$841$	−18.4629	−0.636651
$842$	15.4824	0.533557
$843$	13.1177	0.451798
$844$	−12.0269	−0.413982
$845$	3.48601	0.119922
$846$	−6.23755	−0.214451
$847$	8.75501	0.300826
$848$	−12.8340	−0.440721
$849$	−7.04000	−0.241612
$850$	−12.8078	−0.439304
$851$	8.17722	0.280311
$852$	8.58057	0.293966
$853$	−39.6167	−1.35645	−0.678226	−	0.734854i	$-0.737251\pi$
$853$	−39.6167	−1.35645	−0.678226	+	0.734854i	$0.737251\pi$
$854$	−0.824679	−0.0282199
$855$	0	0
$856$	3.81753	0.130480
$857$	−7.12159	−0.243269	−0.121634	−	0.992575i	$-0.538814\pi$
$857$	−7.12159	−0.243269	−0.121634	+	0.992575i	$0.538814\pi$
$858$	4.95572	0.169186
$859$	29.1935	0.996069	0.498035	−	0.867157i	$-0.334055\pi$
$859$	29.1935	0.996069	0.498035	+	0.867157i	$0.334055\pi$
$860$	−35.5544	−1.21239
$861$	−2.46979	−0.0841703
$862$	35.0740	1.19463
$863$	49.4830	1.68442	0.842211	−	0.539148i	$-0.181254\pi$
$863$	49.4830	1.68442	0.842211	+	0.539148i	$0.181254\pi$
$864$	4.89716	0.166605
$865$	−19.0647	−0.648218
$866$	−5.19189	−0.176428
$867$	−13.3354	−0.452895
$868$	−3.56993	−0.121171
$869$	20.7211	0.702914
$870$	10.9403	0.370911
$871$	12.7844	0.433182
$872$	−1.99936	−0.0677068
$873$	−20.1911	−0.683366
$874$	0	0
$875$	4.30041	0.145380
$876$	−16.2036	−0.547471
$877$	43.8562	1.48092	0.740459	−	0.672102i	$-0.234608\pi$
$877$	43.8562	1.48092	0.740459	+	0.672102i	$0.234608\pi$
$878$	−31.1879	−1.05254
$879$	−4.53110	−0.152830
$880$	−17.8688	−0.602356
$881$	28.3826	0.956236	0.478118	−	0.878296i	$-0.341319\pi$
$881$	28.3826	0.956236	0.478118	+	0.878296i	$0.341319\pi$
$882$	−13.7784	−0.463944
$883$	7.24457	0.243799	0.121900	−	0.992542i	$-0.461101\pi$
$883$	7.24457	0.243799	0.121900	+	0.992542i	$0.461101\pi$
$884$	1.79074	0.0602292
$885$	−40.9252	−1.37569
$886$	3.69892	0.124268
$887$	−17.6920	−0.594038	−0.297019	−	0.954872i	$-0.595993\pi$
$887$	−17.6920	−0.594038	−0.297019	+	0.954872i	$0.595993\pi$
$888$	−1.03117	−0.0346038
$889$	0.00131067	4.39584e−5 0
$890$	50.0287	1.67697
$891$	−7.49004	−0.250926
$892$	−7.55163	−0.252847
$893$	0	0
$894$	−17.5782	−0.587904
$895$	60.0229	2.00635
$896$	−0.573182	−0.0191487
$897$	7.41236	0.247491
$898$	−35.9049	−1.19816
$899$	20.2176	0.674294
$900$	−14.7714	−0.492379
$901$	−22.9823	−0.765653
$902$	−22.8452	−0.760661
$903$	−5.65195	−0.188085
$904$	14.9780	0.498162
$905$	−8.73134	−0.290240
$906$	0.894016	0.0297017
$907$	19.8984	0.660715	0.330358	−	0.943856i	$-0.392831\pi$
$907$	19.8984	0.660715	0.330358	+	0.943856i	$0.392831\pi$
$908$	−7.93349	−0.263282
$909$	−19.4895	−0.646426
$910$	−1.99811	−0.0662368
$911$	25.8071	0.855026	0.427513	−	0.904009i	$-0.359390\pi$
$911$	25.8071	0.855026	0.427513	+	0.904009i	$0.359390\pi$
$912$	0	0
$913$	−63.2495	−2.09325
$914$	−4.74688	−0.157013
$915$	4.84910	0.160306
$916$	27.6864	0.914786
$917$	2.33689	0.0771708
$918$	8.76954	0.289438
$919$	−9.29086	−0.306477	−0.153239	−	0.988189i	$-0.548970\pi$
$919$	−9.29086	−0.306477	−0.153239	+	0.988189i	$0.548970\pi$
$920$	−26.7266	−0.881150
$921$	−11.4130	−0.376071
$922$	−0.00970915	−0.000319754 0
$923$	8.87515	0.292129
$924$	−2.84053	−0.0934465
$925$	7.62836	0.250819
$926$	14.1936	0.466432
$927$	12.6257	0.414683
$928$	3.24609	0.106558
$929$	31.0222	1.01781	0.508903	−	0.860824i	$-0.330051\pi$
$929$	31.0222	1.01781	0.508903	+	0.860824i	$0.330051\pi$
$930$	20.9912	0.688328
$931$	0	0
$932$	7.47943	0.244997
$933$	7.73686	0.253293
$934$	19.6259	0.642180
$935$	−31.9983	−1.04646
$936$	2.06528	0.0675058
$937$	17.7981	0.581440	0.290720	−	0.956808i	$-0.406105\pi$
$937$	17.7981	0.581440	0.290720	+	0.956808i	$0.406105\pi$
$938$	−7.32777	−0.239260
$939$	13.0443	0.425683
$940$	−10.5284	−0.343399
$941$	56.4127	1.83900	0.919502	−	0.393086i	$-0.128593\pi$
$941$	56.4127	1.83900	0.919502	+	0.393086i	$0.128593\pi$
$942$	−18.3220	−0.596963
$943$	−34.1699	−1.11272
$944$	−12.1429	−0.395218
$945$	−9.78508	−0.318309
$946$	−52.2795	−1.69975
$947$	4.17295	0.135603	0.0678013	−	0.997699i	$-0.478402\pi$
$947$	4.17295	0.135603	0.0678013	+	0.997699i	$0.478402\pi$
$948$	−3.90829	−0.126935
$949$	−16.7599	−0.544050
$950$	0	0
$951$	22.2896	0.722791
$952$	−1.02642	−0.0332665
$953$	16.2256	0.525598	0.262799	−	0.964851i	$-0.415354\pi$
$953$	16.2256	0.525598	0.262799	+	0.964851i	$0.415354\pi$
$954$	−26.5058	−0.858156
$955$	−22.4502	−0.726470
$956$	14.9897	0.484800
$957$	16.0867	0.520011
$958$	−20.8569	−0.673855
$959$	−0.148355	−0.00479064
$960$	3.37030	0.108776
$961$	7.79145	0.251337
$962$	−1.06657	−0.0343876
$963$	7.88427	0.254067
$964$	3.63720	0.117146
$965$	−1.22259	−0.0393566
$966$	−4.24863	−0.136697
$967$	8.33229	0.267948	0.133974	−	0.990985i	$-0.457226\pi$
$967$	8.33229	0.267948	0.133974	+	0.990985i	$0.457226\pi$
$968$	−15.2744	−0.490938
$969$	0	0
$970$	−34.0808	−1.09427
$971$	31.1940	1.00106	0.500532	−	0.865718i	$-0.333138\pi$
$971$	31.1940	1.00106	0.500532	+	0.865718i	$0.333138\pi$
$972$	16.1042	0.516542
$973$	−7.69125	−0.246570
$974$	26.1602	0.838226
$975$	6.91484	0.221452
$976$	1.43877	0.0460540
$977$	44.3550	1.41904	0.709520	−	0.704685i	$-0.248912\pi$
$977$	44.3550	1.41904	0.709520	+	0.704685i	$0.248912\pi$
$978$	8.13579	0.260154
$979$	73.5627	2.35108
$980$	−23.2568	−0.742910
$981$	−4.12924	−0.131836
$982$	37.0128	1.18113
$983$	18.3796	0.586218	0.293109	−	0.956079i	$-0.405310\pi$
$983$	18.3796	0.586218	0.293109	+	0.956079i	$0.405310\pi$
$984$	4.30892	0.137363
$985$	63.9508	2.03764
$986$	5.81292	0.185121
$987$	−1.67366	−0.0532733
$988$	0	0
$989$	−78.1954	−2.48647
$990$	−36.9040	−1.17289
$991$	22.7970	0.724172	0.362086	−	0.932145i	$-0.382065\pi$
$991$	22.7970	0.724172	0.362086	+	0.932145i	$0.382065\pi$
$992$	6.22828	0.197748
$993$	−11.1272	−0.353111
$994$	−5.08707	−0.161352
$995$	−46.7482	−1.48202
$996$	11.9297	0.378008
$997$	35.0642	1.11049	0.555247	−	0.831685i	$-0.312624\pi$
$997$	35.0642	1.11049	0.555247	+	0.831685i	$0.312624\pi$
$998$	−29.0035	−0.918088
$999$	−5.22317	−0.165254

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9386.2.a.bw.1.10		15
19.14	odd	18		494.2.x.d.443.4	yes	30
19.15	odd	18		494.2.x.d.339.4	✓	30
19.18	odd	2		9386.2.a.bz.1.6		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.x.d.339.4	✓	30	19.15	odd	18
494.2.x.d.443.4	yes	30	19.14	odd	18
9386.2.a.bw.1.10		15	1.1	even	1	trivial
9386.2.a.bz.1.6		15	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9386.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.966809 q^{3} +1.00000 q^{4} +3.48601 q^{5} -0.966809 q^{6} +0.573182 q^{7} -1.00000 q^{8} -2.06528 q^{9} -3.48601 q^{10} -5.12586 q^{11} +0.966809 q^{12} +1.00000 q^{13} -0.573182 q^{14} +3.37030 q^{15} +1.00000 q^{16} +1.79074 q^{17} +2.06528 q^{18} +3.48601 q^{20} +0.554157 q^{21} +5.12586 q^{22} +7.66683 q^{23} -0.966809 q^{24} +7.15223 q^{25} -1.00000 q^{26} -4.89716 q^{27} +0.573182 q^{28} -3.24609 q^{29} -3.37030 q^{30} -6.22828 q^{31} -1.00000 q^{32} -4.95572 q^{33} -1.79074 q^{34} +1.99811 q^{35} -2.06528 q^{36} +1.06657 q^{37} +0.966809 q^{39} -3.48601 q^{40} -4.45685 q^{41} -0.554157 q^{42} -10.1992 q^{43} -5.12586 q^{44} -7.19958 q^{45} -7.66683 q^{46} -3.02020 q^{47} +0.966809 q^{48} -6.67146 q^{49} -7.15223 q^{50} +1.73130 q^{51} +1.00000 q^{52} -12.8340 q^{53} +4.89716 q^{54} -17.8688 q^{55} -0.573182 q^{56} +3.24609 q^{58} -12.1429 q^{59} +3.37030 q^{60} +1.43877 q^{61} +6.22828 q^{62} -1.18378 q^{63} +1.00000 q^{64} +3.48601 q^{65} +4.95572 q^{66} +12.7844 q^{67} +1.79074 q^{68} +7.41236 q^{69} -1.99811 q^{70} +8.87515 q^{71} +2.06528 q^{72} -16.7599 q^{73} -1.06657 q^{74} +6.91484 q^{75} -2.93805 q^{77} -0.966809 q^{78} -4.04246 q^{79} +3.48601 q^{80} +1.46123 q^{81} +4.45685 q^{82} +12.3393 q^{83} +0.554157 q^{84} +6.24253 q^{85} +10.1992 q^{86} -3.13835 q^{87} +5.12586 q^{88} -14.3513 q^{89} +7.19958 q^{90} +0.573182 q^{91} +7.66683 q^{92} -6.02155 q^{93} +3.02020 q^{94} -0.966809 q^{96} +9.77646 q^{97} +6.67146 q^{98} +10.5863 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{8} + 18 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} + 15 q^{16} + 3 q^{17} - 18 q^{18} + 3 q^{20} - 33 q^{21} + 3 q^{22} + 9 q^{23}+ \cdots + 3 q^{98}+O(q^{100}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 3 * q^5 + 3 * q^6 - 15 * q^8 + 18 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 + 15 * q^16 + 3 * q^17 - 18 * q^18 + 3 * q^20 - 33 * q^21 + 3 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 15 * q^26 - 42 * q^27 - 12 * q^29 - 24 * q^31 - 15 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 + 18 * q^36 - 30 * q^37 - 3 * q^39 - 3 * q^40 + 24 * q^41 + 33 * q^42 - 12 * q^43 - 3 * q^44 + 21 * q^45 - 9 * q^46 - 6 * q^47 - 3 * q^48 - 3 * q^49 - 24 * q^50 - 48 * q^51 + 15 * q^52 - 9 * q^53 + 42 * q^54 - 60 * q^55 + 12 * q^58 - 12 * q^59 - 12 * q^61 + 24 * q^62 + 15 * q^63 + 15 * q^64 + 3 * q^65 - 3 * q^66 - 48 * q^67 + 3 * q^68 - 18 * q^69 - 6 * q^70 - 21 * q^71 - 18 * q^72 + 21 * q^73 + 30 * q^74 - 21 * q^75 - 9 * q^77 + 3 * q^78 - 45 * q^79 + 3 * q^80 + 15 * q^81 - 24 * q^82 - 33 * q^83 - 33 * q^84 - 6 * q^85 + 12 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 - 21 * q^90 + 9 * q^92 - 3 * q^93 + 6 * q^94 + 3 * q^96 + 24 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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